Like classic bits, we also can define multiple qubits.
For one \(b\) -qubit, its states are unit vectors in a \(2^b\) -dimensional complex vector space with computational basis states of the form \(|x_1 x_2 \cdots x_b \rangle \) , \(x_j=0\)  or 1, \(j=1,\ldots , b\) .
For example, the states of 2-qubit are unit vectors in \(\mathbb {C}^4\)  space with the superposition states
\(|\psi \rangle = \alpha _{00}\,|00\rangle + \alpha _{01}\,|01\rangle + \alpha _{10} \,|10\rangle + \alpha _{11} \,|11\rangle \) , where amplitudes \(\alpha _x\)  are complex numbers satisfying \(|\alpha _{00}|^2 + |\alpha _{01}|^2 + |\alpha _{10}|^2 + |\alpha _{11}|^2 =1\) .
Similar to the single qubit case, we obtain a measurement outcome \(x\)  as one of the \(00,01,10,11\)  with a corresponding probability \(| \alpha _x^2|\) .
The quantum exponential complexity is then shown in the exponential growth of dimensionality \(2^b\)  and the number of \(2^b\)  amplitudes needed to specify the superposition states.
Thus, as the quantum systems evolves, they are able to store and keep track an exponential number of complex numbers while performing data manipulations and calculations.
See [1]} and [2]} for details.
